By Robert Young
By Sergey Yurkevich
Appears in collection : Not Only Scalar Curvature Seminar
Many manifolds are (positive) scalar curvature rigid: one can't increase the scalar curvature without shrinking the manifold. The first of these results was established by Llarull (for the round spheres), using spinorial techniques. We discuss the problem and the known solutions, including current research questions around this topic.